A014572 Continued fraction for Thue-Morse constant.

0, 2, 2, 2, 1, 4, 3, 5, 2, 1, 4, 2, 1, 5, 44, 1, 4, 1, 2, 4, 1, 1, 1, 5, 14, 1, 50, 15, 5, 1, 1, 1, 4, 2, 1, 4, 1, 43, 1, 4, 1, 2, 1, 3, 16, 1, 2, 1, 2, 1, 50, 1, 2, 424, 1, 2, 5, 2, 1, 1, 1, 5, 5, 2, 22, 5, 1, 1, 1, 1274, 3, 5, 2, 1, 1, 1, 4, 1, 1, 15, 154, 7, 2, 1, 2, 2, 1, 2, 1, 1, 50

Offset

0,2

Links

Harry J. Smith, Table of n, a(n) for n = 0..20000

M. Beeler, R. W. Gosper, and R. Schroeppel, HAKMEM. Cambridge, MA: Mass. Institute of Technology Artificial Intelligence Laboratory, Memo AIM-239, Feb. 1972, Item 122, page 56.  Also HTML transcription.

Y. Bugeaud, On the rational approximation to the Thue-Morse-Mahler numbers, Ann. Inst. Fourier, Grenoble, 61 (2011), pp. 2065-2076. See p. 2068.

Y. Bugeaud and M. Queffélec, On Rational Approximation of the Binary Thue-Morse-Mahler Number, Journal of Integer Sequences, 16 (2013), #13.2.3.

Eric Weisstein's World of Mathematics, Thue-Morse Constant.

G. Xiao, Contfrac

Index entries for continued fractions for constants

Example

A014571 = 0.4124540336401075977833613... = 0 + 1/(2 + 1/(2 + 1/(2 + 1/(1 + ...)))). - Harry J. Smith, Apr 25 2009

Mathematica

P = Sum[If[OddQ[Count[IntegerDigits[n, 2], 1]], 2^(-n-1), 0], {n, 0, 400}]; ContinuedFraction[P, 91] (* Jean-François Alcover, Oct 23 2012 *)
(* ThueMorse function needs $Version >= 10.2 *)
P = FromDigits[{ThueMorse /@ Range[0, 400], 0}, 2];
ContinuedFraction[P, 91] (* Jean-François Alcover, Jan 30 2020 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 21000); x=0.0; m=70000; for (n=1, m-1, x=x+x; x=x+sum(k=0, length(binary(n))-1, bittest(n, k))%2); x=x/2^m; y=contfrac(x); for (n=1, 20001, write("b014572.txt", n-1, " ", y[n])); } \\ Harry J. Smith, Apr 25 2009

Crossrefs

Cf. A014571.

Sequence in context: A239209 A180824 A105777 * A071458 A247719 A131308

Adjacent sequences: A014569 A014570 A014571 * A014573 A014574 A014575

Keyword

nonn,cofr

Author

Eric W. Weisstein

Status

approved